Find the product of all positive integral values of \(n\) such that \(n^2-35n+306= p\) for some prime number \(p\). Note that there is at least one such \(n\).
This problem seems tricky at first, if you plug in any positive integer, you will always get an even number. There is only one even prime which is 2. When n=16,19, p=2 which are the only values that work. So 16*19= 304 which is your answer.
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